Question #105310

The speed of a particle changes from √5m/s to 2√5m/s in a time 't' . If the magnitude of change in its velocity is 5m/s the angle between the initial and final velocities of the particle is

Ans:90°

Ans:90°

Expert's answer

Initial speed"=\\sqrt{5} m\/sec"

Final speed "=2\\sqrt{5} m\/sec"

And magnitude of change in velocity is "5m\/sec" which is equal to "\\sqrt{(\\sqrt{5})^2+({2\\sqrt{5}})^2}" which means that magnitude in change of velocity is the unique case with velocities at different states do not have components in a common direction.

For example,Initial velocity"=\\sqrt{5}\\hat {i}"

Final velocity"=2\\sqrt{5} \\hat{j}"

Magnitude of change in velocity"=|2\\sqrt{5}\\hat{j}-\\sqrt{5}\\hat{i}|=\\sqrt{(\\sqrt{5})^2+({2\\sqrt{5}})^2}=5m\/sec"

Dot product of initial and final velocities"=(\\sqrt{5}\\hat{i}).(2\\sqrt{5}\\hat{j})=0"

or we can say the velocity at different states are perpendicular to each other or angle between them is "90\\degree."

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